(4k²+2k+1)+(-4k²+2k-1)

To simplify the given expression, we need to combine like terms:

(4k² + 2k + 1) + (-4k² + 2k - 1)

Combining the like terms, we add the coefficients of k², k, and the constant term:

(4k² + (-4k²)) + (2k + 2k) + (1 + (-1))

This simplifies to:

0k² + 4k + 0

Since 0 multiplied by any number is 0, the k² term disappears:

0 + 4k + 0

Finally, we're left with:

4k